The phone is probably locked...
Aren't couples know each other's passwords? And Sooha didn't mention the phone was locked.
Not always. And usually phones are locked
Phones always are locked and usually we know our partner/spouse passwords. And when Shooha mentions Taesoo didn't take his phone, wouldn't she mention why Taesoo's phone is locked? Or why she shouldn't know the password? I think it's author's plan just to give Doh another chance to come back with a kind heart and also to get our sympathy on poor jobless Doh.
It's not usually like that honestly. More like it depends on the people and it's not really necessary. If she knew his password, she would know about a lot of stuff that she didn't, not only where he lives of his little brother's number.
Didn't he leave his phone at Sooha's place? Then, why not calling his family or brother's number? Why asking Doh? Is it going to be a valid excuse for Doh to come back to Joo's- don't know the rest of his name- life back?